I'm not sure what your circumstances are (adopted?) but here are a few ideas:
If you're adopted, get your records unsealed (a judge can do this) and your original birth certificate should be among the papers. This will provide a lot of clues you can follow.
Once you have your original birth certificate, check in very old Crisscross directories to see who lived near the address shown on the birth certificate. Then see if the current residents are the same (or possibly related). Sometimes old neighbors know where someone may have gone, or who they were related to.
Look for the maiden name on the birth certificate, and use that to track down possible relatives. If you locate a Crisscross directory for the approximate year you were born (you can often find these through libraries), you can look for possible relatives living in the town/city at the same time, and then contact those with similar names in the current directory.
If you aren't in the same city where you were born, call the library there; many reference librarians are happy to help with these searches.
Some (older) birth certificates show the occupation of a parent. I know of someone whose friend tracked down her birth parents through the clue that her father was listed as a floor layer. At the time she was born, there wouldn't have been that many flooring firms in the town where she was born. The friend obtained a phone directory for that city and found a flooring firm with an ad stating how many years they were in business. Sure enough, because that skill is specialized, everyone in town new each other and someone actually knew her father, even though he was retired. Her father was then the connection to finding her mother.
Can you contact your father? See if he has clues you can follow.
Good luck - I've known people who have tracked down people after many decades. I hope you can find your mother!